64 (number)

64 (sixty-four) is the natural number following 63 and preceding 65.

In mathematics

Sixty-four is the square of 8, the cube of 4, and the sixth power of 2. It is the smallest number with exactly seven divisors. It is the lowest positive power of two that is adjacent to neither a Mersenne prime nor a Fermat prime. 64 is the sum of Euler's totient function for the first fourteen integers. It is also a dodecagonal number^[1] and a centered triangular number.^[2] 64 is also the first whole number that is both a perfect square and a perfect cube.

Since it is possible to find sequences of 64 consecutive integers such that each inner member shares a factor with either the first or the last member, 64 is an Erdős–Woods number.^[3]

In base 10, no integer added up to its own digits yields 64, hence it is a self number.^[4]

64 is a superperfect number—a number such that σ(σ(n)) = 2n.^[5]

64 is the index of Graham's number in the rapidly growing sequence 3↑↑↑↑3, 3 ↑^{3↑↑↑↑3} 3,…

In science

• The atomic number of gadolinium, a lanthanide

Astronomy

• Messier object M64, a magnitude 9.0 galaxy in the constellation Coma Berenices, also known as the Black Eye Galaxy.
• The New General Catalogue object NGC 64, a barred spiral galaxy in the constellation Cetus.
• The Saros number of the solar eclipse series which began on -832 April 11 and ended on 430 May. The duration of Saros series 64 was 1262.1 years, and it contained 71 solar eclipses.
• The Saros number of the lunar eclipse series which began on -801 August 9 and ended on 714 February. The duration of Saros series 64 was 1514.5 years, and it contained 85 lunar eclipses.

In other fields

A chessboard has 64 squares

Sixty-four is:

• In some computer programming languages, the size in bits of certain data types
• In chess or draughts, the total number of black (dark) and white (light) squares on the game board
• The total number of gems in a standard Bejeweled game board
• 64 is the name of a Russian chess magazine
• The code for international direct dial calls to New Zealand
• The designation of US Interstate 64, a freeway from Missouri to Virginia
• The designation of U.S. Route 64, a highway from Arizona to North Carolina
• The subject of the Beatles song "When I'm Sixty-Four"
• The registry of the U.S. Navy's aircraft carrier USS Constellation (CV-64)
• The number of Braille characters in the old 6-dot system
• In 8-bit home computers, a common shorthand for the Commodore 64
• In video games, the Nintendo 64 video game console and (historically) the Commodore 64. Since 1996, the number 64 has been an abbreviation or slang for Nintendo 64 (though N64 is more common) along with the games Super Mario 64, Mario Kart 64 and more along with 64 being used in the term Super Smash 64 which is used to distinguish Super Smash Bros (video game) from the name of the series (Super Smash Bros)
• The maximum number of strokes in any Chinese character
• Number of hexagrams in the I Ching
• Number of sexual positions in the Kama Sutra
• Number of demons in the Dictionnaire Infernal
• Slang term referring to a 1964 Chevrolet Impala, often configured as a lowrider, a popular subject among early-90's gangsta rap
• The number of classical arts listed in many Indian scriptures. They include: singing, dancing, painting, poetry, playing cards, making arguments, making flower garlands, etc.
• The number of the French department Pyrénées-Atlantiques
• The number of crayons in the popular Crayola 64 pack
• Base 64 is used for example with Base64 encoding.
• Maximum stack size in the video game Minecraft, in non-command situations.
• 64 (dog) is a character in the Donald Duck comics universe.
• Number of codons in the RNA codon table under genetic code.
• Number of golden disks in the myth of the Tower of Hanoi.
• A number referring to Tiananmen Square protests of 1989 (Chinese: 六四事件; literally: "Six Four Incident") in Chinese
• "64" is the title of a song by the hip-hop group Mellowhype from their album Blackenedwhite

See also

• The 64,000 Dollar Question

References